This invention relates to methods and apparatus for processing product (rectangular) error correction-coded (ECC) data arrays, and more particularly to increasing the processing speed of such methods and apparatus where the arrays are jointly affected by random error and erasure.
In the prior art, digital versatile disk or alternatively digital video disc (DVD) optical storage technology has received significant attention. In this regard, DVD is similar to that of a CD-ROM. However, it possesses a substantially greater storage capacity. Structurally, a DVD uses a single spiral track on a reflective metal surface packaged in plastic. The spiral track contains pits that are read by a drive laser as values of one or zero bits. DVD increases the data capacity of the disk by increasing the pit density and the number of tracks. As the pits become smaller and more densely packed, a smaller laser is required to read the disk. DVD uses a 635-nanometer laser compared with a 780-nanometer laser on the standard CD-ROM. Current laser support doubles the pits per track, and doubles the tracks per surface area available on a CD-ROM. DVD further increases capacity by using a more efficient sector format. The base capacity of DVD disks is 4.7 GB (single side/single layer), while the capacity of the CD-ROM use is in the order of 650 MB.
It is also well known in the prior art to use finite field, algebraic, block, or cyclic codes for detecting and correcting multiple bytes in error in long byte strings read back from a cyclic, concentric, tracked storage medium such as a magnetic disk storage subsystem or the like. Typically, each byte string of predetermined length is treated as if it were an algebraic polynomial and subject to modulo division by an encoding polynomial. If the code is denominated as being xe2x80x9csystematicxe2x80x9d, then redundant bytes derived from the data are appended to the data string which otherwise remains intact. In the case of linear block codes, the remainder is appended to the end of the data byte string. Each data byte string plus the appended remainder is then recorded on a storage medium or transmitted. Subsequently, when the data is accessed and played back from the medium, a remainder is in principle recalculated from the datastream as it is extracted and compared with the recorded remainder. If the remainder values comparison match, the difference result is zero. If the results do not match (nonzero difference), then this is indicative or error or erasure. The codes are quite advanced such that the remainders are processed not only for identifying the presence of error, but also for pinpointing its location and determining the correction values to be applied to the datastream. This is termed syndrome processing. Codes useful for error detection and correction are called xe2x80x9cECCxe2x80x9d codes.
A Reed-Solomon (RS) code exemplifies linear cyclic ECC codes used extensively in magnetic recording and communications. One advantage of RS codes is that they maintain maximum distance among codewords for any given length of data. This xe2x80x9cspacingxe2x80x9d between permissible codewords renders them useful for detecting and correcting randomly occurring byte errors as well as burst errors over a run of contiguous bytes. Reference should be made to Hassner et al., copending application Ser. No. 08/838,375; now U.S. Pat. No. 5,942,005 xe2x80x9cMethod and Means for Computationally Efficient Error and Erasure Correction in Linear Cyclic Codesxe2x80x9d, filed Apr. 8, 1997, for a detailed description of a high-performance ECC detection and correction method and apparatus embedded in the recording channel path of a magnetic disk storage subsystem.
The RS code among other ECC codes is one dimensional in that it is defined over a data byte string of predetermined length. Such encoding is adequate for one-dimensional data recording or transmission such as is found on concentric, tracked magnetic disk storage. However, optical recorded images are recorded as data arrays. In this mode, so-called product or rectangular codes suitable for protecting data arrays have been extant for some time.
A product-coded data array as defined in Lin et al., xe2x80x9cError Control Coding: Fundamentals and Applicationsxe2x80x9d, Prentice-Hall, Inc., copyright 1983, at pp. 274-278, comprises a data array or rectangle of data bytes in which K1 rows and K2 columns are formed. Then, a horizontal ECC code of PI bytes is appended to each row and a vertical code of PO bytes is appended to each column. This results in an array of dimensions (K1+PI)xc3x97(K2+P0). The rate (k/n) of the rectangular code is:
k/n=(K1xc3x97K2)/(K+P1)(K2+P0).
When the data is read from any storage system, the data bytes are subject to error and erasure from random, intermittent, recurrent sources. These may be due to media defects, signal coupling between tracks, extraneous signals induced in the readback path, etc. In the case of a one-dimensional data array such as a row vector, error patterns may occur as random bytes in error or clustered together as a run of contiguous bytes in error. One related consequence is the fact that as the number of errors in any given row increase, then the likelihood of miscorrection by the ECC decoder increases. As Lin et al. point out at page 275, in a product-coded, two-dimensional array, one process of error detection and correction involves first error decoding the rows and then error decoding the columns. If the density of errors is relatively low, then row correction might be sufficient. However, if the density in some portions of some rows is high, then row error decoding might result in the old errors being cured and new errors being created.
It is generally desired to correct the errors in place. This means that an array is read from the medium and written into a sufficiently sized buffer or RAM and memory local to the storage subsystem. One processing problem is that the local buffer or RAM must be repeatedly referenced in the column as well as row directions. This substantially increases both decoding time and complexity in the processing of errors and erasures.
It is an object of this invention to devise a method and apparatus for detecting and correcting errors and erasures in product-coded data arrays.
It is a related object to devise a method and apparatus for error and erasure detection and correction of systematic ECC product-coded data arrays as used in DVD or other optically readable data recording subsystems.
It is yet another object that such method and apparatus efficiently effectuate detection and correction of errors and erasures of the ECC product-coded data array in place as imaged from a storage or communications source into a buffer or RAM local to said source.
For purposes of this invention, each syndrome-detected xe2x80x9cerrorxe2x80x9d connotes an unknown syndrome value change of one or more symbols at an unknown location or position within an array row. Relatedly, each syndrome-detected xe2x80x9cerasurexe2x80x9d connotes the fact that while the value of the change is unknown, the location and position within the array are known.
It was unexpectedly observed that if the statistics of miscorrection were taken into account on a row basis, then an erasure should be defined as the occurrence of three or more contiguous errors in a row. It was further observed that the processing speed of the arrays could be enhanced if rows containing random errors could be processed in the row direction and erasure processing deferred until processing of the columns. It was relatedly observed that row and column processing necessarily involved scanning and forming a dense map identifying the error locations and correction values after which the correction could be effectuated as indexed by the dense map.
Thus, a systematic ECC product-coded data array is read from storage or from a communications source and is written into a local buffer or RAM and scanned in row major order. Concurrently, a dense map of rows is formed containing random errors and their correction values. Also, pointers to rows containing erasures are generated and saved. Next, the random errors are corrected in the array in place in the buffer or memory by logically combining the map-stored corrections with the counterpart array value. The second phase involves column correction. This involves scanning the array in column major order to form a second dense map of columns in which the columns containing erasure corrections are clustered together, and the columns containing corrections for random errors only are clustered together. The pointers to the rows identify the columns containing erasure errors, and the erasure corrections are determined using pairwise adjacent row values and placed in the map.
The correction of columns proceeds in column major order. This means the columns containing erasure-only errors or mixed erasure and random errors are first processed. When this has been completed, the columns containing only random errors are processed. The logic of this process assumes that most random errors will be resolved during row processing. It is anticipated, however, that occasionally miscorrection during row processing will occur. This will result in a random error distribution over some rows of the array. Thus, some array columns will contain either erasure-only error, mixed erasure or random error, or random-only error. In those columns containing erasure-only and mixed erasure and random error terms, the erasure corrections are first determined with reference to the pair adjacent row terms. Next, the random error terms are ascertained by processing the ECC bytes defined over that column. The columns containing erasure-only or mixed errors are then corrected with reference to the second. Lastly, an extension map;covering the remaining columns containing only random errors is built, and the corrections calculated and then applied to the counterpart columns in column major order to complete the process.
More particularly, the above objects are satisfied by a machine-implementable method for detecting and correcting errors and erasures by a processor in systematic product linear block or cyclic error correction-coded (ECC) data arrays written into a memory, the processor being capable of accessing the memory. The method comprises the steps of (a) iteratively syndrome processing the array data in row major order, and (b) iteratively syndrome processing the array data in column major order.
The first step includes forming a first map classifying each row containing location indicia of random errors, their correction patterns, and pointers to rows containing erasure errors. It further includes effectuating row array random error corrections in place in memory according to the first map. In a similar vein, the second step includes forming a second map containing location indicia and correction patterns for each pair adjacent position within each column containing erasure errors as indexed by a counterpart row pointer. An extension of the second map is also formed but it is to obtain location indicia within each column containing random errors and their correction patterns. The second step necessarily includes effectuating column array erasure corrections and random error corrections in place in memory according to the second map.